5 Answers
5

Cure spells work on creatures: constructs are creatures. However, all of the curative spells in the PHB (I think) specifically say they don't work on constructs or undead; this is not a general rule though.

Medicine works on "your companions": with a certain generosity of spirit, this extends to construct companions. Medicine allows you to stabilise or diagnose a disease. Since all constructs so far described are destroyed at 0hp, you can't stabilise those specific constructs. Nothing stops a construct contracting a disease, however, constructs are likely immune to organic disease; magical and construct only diseases are possible.

As to what it looks like: that's up to you.

So in general, yes, however, the specific cure spells and specific constructs so far published limit the general application.

Warforged and Shardminds are races very specific to the Eberron campaign setting.

There is no official 5e material as of this writing, but there is an Unearthed Arcana with a first draft of Warforged on the Wizards site. From that article:

Living Construct. Even though you were constructed, you are a living
creature. You are immune to disease. You do not need to eat or
breathe, but you can ingest food and drink if you wish.

It's not 100% clear if the line "living creature" means that you bypass the "construct" nature. That stated, the constructs in the MM have a large set of Immunities not given to the Warforged. So there's clearly a difference between them and "normal" constructs.

If you don't quite like the Unearthed Arcana version, there are several more "community" version here. Sadly, they use similar wording and offer no clarity.

As a DM, you're likely creating these races, so this decision is really up to you.

The easiest way to do this is to treat them like other humanoids and let everything work as normal. The Unearthed Arcana wording says they are immune to disease, but they can still be poisoned or charmed, etc. So they probably get disadvantage on a save vs. Shatter, but they otherwise interact with Necromancy in the same way as other races.

If you want to make them harder to heal, I would suggest being explicit and making it a racial trait rather than relying on their "construct" nature. Given them something like "anything normally requiring a Medicine check instead requires an Arcana check with the same DC" & "when receiving healing from a spell, they only receive healing if the caster also knows the Mending spell".

If you rely on their "construct" nature, you will have to go through a lot of decisions on how spells work. Does Raise Dead work? What about Animate Dead? What about Animate Object?

Treating a PC as full-on construct goes beyond just healing. So I would tread that lightly.

Constructs are made, not born. Some are programmed by their creators
to follow a simple set of instructions, while others are imbued with
sentience and capable of independent thought. Golems are the iconic
constructs. Many creatures native to the outer plane of Mechanus, such
as modrons, are constructs shaped from the raw material of the plane
by the will of more powerful creatures.

The description of the warforged race in the Wayfinder's Guide to Eberron (p. 67) says, under the "Living Steel and Stone" heading (emphasis mine):

While they’re formed from stone and steel, warforged are living humanoids. Resting, healing magic, and the Medicine skill all provide the same benefits to warforged that they do to other humanoids.

\$\begingroup\$Welcome to RPG.SE! Take the tour if you haven't already. Note that this question was asked in 2016, after the release of UA: Eberron, in which warforged first appeared with the "Living Construct" trait.\$\endgroup\$
– V2Blast♦Jan 19 '19 at 5:42

No to cure, maybe to medicine

Cure Wounds states, "This spell has no effect on undead or constructs", so it's out.

Medicine lets you stabilize dying companions or diagnose an illness. The illness part isn't going to help as a warforged's Living Construct trait makes them immune to disease. They can be dying though so the RAW says you help them out. RAI I think this makes sense as if a construct is able to be, "dying", somehow perhaps the general medical techniques (keep the fluids from coming out) would still apply.

\$\begingroup\$But are 'living constructs' grouped in with 'constructs', or are they separate? Both undead and constructs are linked in that they are not alive but are merely animated, so that could be why Cure Wounds won't work on them. But living constructs are alive, so is that the deciding factor for whether cure spells work on them?\$\endgroup\$
– ZsoFeb 5 '16 at 22:55

\$\begingroup\$@Zso Living construct is a trait on the warforged. Their type isn't listed by assuming it is construct isn't a stretch\$\endgroup\$
– CeribiaFeb 5 '16 at 23:36

3

\$\begingroup\$This was precisely the confusion I'm having in my current campaign. So far we have ruled that a 'Living Construct' has two types in it's tag. It is BOTH 'Living' and 'Construct' , making it unable to benefit from healing due to the wording of healing spells. I personally think this is NOT what was intended by WotC as EVERY player character race (Notice how they are all humanoids as well) are capable of receiving healing. There are NO redeeming qualities a Warforged have that make up for being unable to be healed by magical means; how could WotC possible have intended that?\$\endgroup\$
– AiratomeFeb 6 '16 at 0:04

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– KorvinStarmastFeb 7 '18 at 15:32